The present invention relates to the transmission of signals through a nonlinear medium. More particularly, the present invention relates to an apparatus and method for eliminating the effects of nonlinearities caused by a nonlinear medium, with exemplary application to optical signals and optical transmission media.
Fiber optic communication generally involves the transmission of high bit-rate digital data over silica glass fiber by modulating a laser or other optical source. As with any data transmission medium, there are ongoing development efforts to increase the data rate through fiber optic media, as well as to increase the practical transmission distance of single fiber optic spans. Although the development of erbium-doped fiber amplifiers (EDFA) has virtually eliminated fiber attenuation as an obstacle to achieving longer transmission distances, group velocity dispersion and optical fiber nonlinearities continue to represent a barrier to increased transmission capability. Optical fiber nonlinearities begin to manifest themselves as the capabilities of the channel are pushed to their limits through the use of increased signal power, higher bit rates, longer transmission distances, and increased numbers of channels.
Fiber nonlinearities place substantial limits on the capacity of wavelength-division multiplexed (WDM) optical communication systems. As described in Chraplyvy, xe2x80x9cLimitations on Lightwave Communications Imposed by Optical-Fiber Nonlinearities,xe2x80x9d Journal of Lightwave Technology, Vol.8, No.10, (1990), p1548-1557, the contents of which are hereby incorporated by reference, these limitations include, but are no limited to: limiting the optical power that can be launched into the fiber; limiting the number of channels in WDM optical communications; limiting the amount of dispersion the fiber may have; and limiting the data bit rate. Various methods to reduce the effect of fiber nonlinearities have been proposed, including the use of lower laser power, unequal channel spacing, and other methods. Generally, however, these methods are directed to individual mechanisms by which certain nonlinearities arise, and are not adapted to eliminate all third-order nonlinearities simultaneously.
FIG. 1 shows a block diagram of a generic nonlinear transmission medium 102 having an input signal E and an output signal Exe2x80x2. For optical media, the signals E and Exe2x80x2 are time functions representing the electric field portion of an optical wave at the relevant point along the signal path. Unless otherwise indicated in the present disclosure, the representations E and Exe2x80x2 may be interchanged with the representations E(t) and Exe2x80x2(t). The nonlinear transmission medium 102, while identified as a fiber optic link in many examples herein, may also be a discrete xe2x80x9cpointxe2x80x9d device such as a semiconductor optical amplifier (SOA), an EDFA amplifier, or generally any optical processing circuit having a nonlinear response characteristic. In such case, the input signal E and transmitted output signal Exe2x80x2 appear very close to each other in space. In summary, the nonlinear transmission medium 102 may have a length that is as long as hundreds of miles or as short as a few nanometers, depending on the specific application.
FIG. 2 shows a timing diagram of an exemplary waveform 202 for E and a corresponding waveform 204 for Exe2x80x2 for the system of FIG. 1. As represented by FIG. 2, the output signal 204 comprises the sum of an attenuated version 206 of E plus an induced nonlinearity 208. The nonlinear mechanisms in optical media causing the nonlinearities include cross-phase modulation (XPM), stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), optically induced birefringence (OIB), parametric four-wave mixing (FWM), self-phase modulation (SPM), and modulation instability (MI). Although further information on these and other nonlinear mechanisms are described in Agrawal, Nonlinear Fiber Optics, Academic Press (2nd ed. 1995), the contents of which are hereby incorporated by reference, the preferred embodiments described herein may be advantageously used regardless of the specific nonlinear mechanisms in effect.
When an optical signal E(t) passes through a nonlinear optical medium, the output signal Exe2x80x2(t) may be expressed as:
Exe2x80x2=xcexa1E+xcexa2EE+xcexa3EEE+xcexa4EEEE+ . . . xe2x80x83xe2x80x83{1}
where xcexa1 denotes the linear input-output response and xcexa2, xcexa3, xcexa4, etc. are tensors representing nonlinear input-output responses. Local nonlinearities due to the physics of the optical material are responsible for the second order (xcexa2) and third order (xcexa3) nonlinearities, while higher order nonlinearities come into effect only for lengthy optical media which display such higher order effects due to the cascading of the local nonlinearities over an extended distance. As known in the art, for systems where the overall dimension of the optical medium is not excessive or the local nonlinearities are weak, the higher order nonlinear effects are negligible. Also as known in the art, in most optical communication and signal processing systems, the even-order nonlinear effects xcexa2, xcexa4, etc. are not of practical concern, because the wave components generated by these even order nonlinearities are associated with very large frequency shifts which move them far away from the signal band, thereby allowing for removal using conventional filtering techniques at the destination. Therefore, a practical representation of the input-output response includes only the dominant third-order nonlinearity term, as shown in Eq. (2):
Exe2x80x2=xcexa1E+xcexa3EEExe2x80x83xe2x80x83{2}
Despite the presence of only a third order nonlinearity in Eq. (2), it is to be appreciated that the preferred embodiments to be described infra are straightforwardly extendible to the cancellation of higher order nonlinearities xcexa5, xcexa7, etc. when they become important. Moreover, the preferred embodiments disclosed herein can also be applied to eliminate even-order nonlinearities xcexa2, xcexa4, etc. where necessary.
In practical optical communication systems using long distance optical fibers with optical amplification by an EDFA amplifier or a semiconductor optical amplifier (SOA), the third order xcexa3-nonlinear effect of Eq. (2) may generate a sizable unwanted term that can significantly distort the input signal E(t). Additionally, in optical amplifiers there is also a cross gain modulation (XGM) effect due to gain saturation in addition to the XPM and FWM effects mentioned supra. In wavelength-division multiplexed (WDM) systems, the unwanted signal xcexa3EEE(t) can lead to serious cross talk and noise level problems. Even in a single wavelength system, the unwanted signal K3EEE(t) may significantly distort the desired signal. Thus, in fiber optic communication systems, optical fiber nonlinearities and similar nonlinear effects in optical amplifiers (SOA or EDFA) and other optical signal processing components have become a major factor in limiting system capacity.
Accordingly, it would be desirable to provide an optical fiber transmission system in which nonlinearities induced by the optical fiber medium are eliminated.
It would be further desirable to provide such an optical fiber transmission system that can be physically realized using known, off-the-shelf optical components.
It would be further desirable to eliminate unwanted nonlinear effects in various optical signal processing systems.
It would be still further desirable to provide a method for eliminating the effects of optical transmission system nonlinearities that can be applied to any nth-order nonlinearity.
It would be still further desirable to eliminate the effects of multiple nonlinearities of many different orders in a transmission medium.
It would be even further desirable to provide a method for eliminating nonlinear effects that can be extended beyond optical systems to any type of signal transmission or processing medium.
It would be even further desirable to provide a method for eliminating nonlinear effects that can be applied to nonlinear media including nonlinear point devices such that discrete, nonlinearity-free optical amplifiers or other discrete, nonlinearity-free optical processing devices may be produced.
In accordance with a preferred embodiment, an apparatus and related method are provided for transmitting an optical signal through a nonlinear medium such that nonlinearities caused by the medium are eliminated from the transmitted optical signal. The optical signal is presumed to have a duty cycle, wherein the optical signal is xe2x80x9conxe2x80x9d during an active portion of the duty cycle and xe2x80x9coffxe2x80x9d during an inactive portion, the inactive portion being of equal or longer duration than the active portion. Briefly stated, the preferred embodiments take advantage of the fact that two signals in a nonlinear medium cannot interfere with each other if they are never xe2x80x9conxe2x80x9d at the same time. Because of this fact, and because the optical signal has a duty cycle with xe2x80x9coffxe2x80x9d times of equal or greater duration than the xe2x80x9conxe2x80x9d times, then the optical signal plus a delayed and weighted version of itself can be transmitted through the nonlinear medium without mutual interference. The transmitted signals can then be re-synchronized, weighted, and subtracted at the other end of the nonlinear medium such that nonlinearities induced by the medium are canceled, but such that a signal proportional to a delayed version of the original optical signal survives.
According to a preferred embodiment, the optical signal is input to a combining interferometer prior to introduction into the nonlinear medium, and then passed though a subtracting interferometer at an output of the nonlinear medium. The combining interferometer is adapted to split the optical signal into a split-beam portion and a direct-beam portion, weight the split-beam portion by a first weighting factor, delay the split-beam portion by a first delay amount, and then recombine the split-beam portion with the direct-beam portion. The first weighting factor may be set to a number other than zero or 1. The first delay factor is set such that the split-beam portion and the direct-beam portion have active portions that are non-overlapping in time. The subtracting interferometer is adapted to split the output of the nonlinear medium into a split-beam portion and a direct-beam portion, weight the split-beam portion by the cube of the. first weighting factor, delay the split-beam portion by the first delay amount, and then subtract the direct-beam portion from the split-beam portion. During intervals corresponding to the active portions of the optical signal, the output of the subtracting interferometer is free from the third-order nonlinearities induced by the nonlinear medium and is directly proportional to a delayed version of the original optical signal. An optional chopper device may be provided to eliminate the extra unused signals that appear during intervals corresponding to the inactive portions of the optical signal.
In another preferred embodiment, the subtracting interferometer comprises an optical time demultiplexer instead of an optical splitter. During intervals corresponding to the active portion, the optical time demultiplexer couples the output of the nonlinear medium to the split-beam path of the subtracting interferometer, whereas during intervals corresponding to the inactive portion, the optical time demultiplexer couples the output of the nonlinear medium to the direct-beam path of the subtracting interferometer. During intervals corresponding to the active portions of the optical signal, the output of the subtracting interferometer is free from the third-order nonlinearities induced by the nonlinear medium and is directly proportional to a delayed version of the original optical signal. However, during intervals corresponding to the inactive portions of the optical signal, the output of the subtracting interferometer is a null value, with no extra unused signals requiring elimination.
Multiple implementations of an apparatus in accordance with the preferred embodiments may be implemented in parallel to achieve nonlinearity-free transmission of an optical signal having a 100 percent duty cycle. Moreover, the preferred embodiments may be generalized beyond eliminating the effects of third order nonlinearities. In particular, an nth-order linearity may be canceled by setting the weighting factor of the subtracting interferometer equal to the weighting factor of the combining interferometer raised to the nth power. Even more generally, multiple nonlinearities may be canceled by adding further split-beam portions and split-beam delays to each of the combining and subtracting interferometers, wherein a set of weights may be selected such that the original signal and a multiplicity of delayed-and-weighted versions of itself are combined to eliminate the multiple-order nonlinearities, while the linear portion of the signal survives. Advantageously, the preferred embodiments may also be applied to the transmission of any type of communication signal through a nonlinear medium, including electromagnetic, acoustic, mechanical, or even neurological signals, provided only that physical realizations of splitters, weighting devices, delay devices, and combiners can exist for that type of signal.